Question

des of an equality by the same non-zero
The root of
sint of 3X-6 = x+2 isha​

Answer 1

Step-by-step explanation:

If α is the root of 2x

3

−3x

2

+6x+6=0 find [α].

∵2x

3

−3x

2

+6x+6=0

f

′

(x) =

dx

d

(2x

3

−3x

2

+6x+6)

=x

2

−x+6

=6(x

2

+x−1)

∵ Discriminent of f

′

(x)<0

Hence f

′

(x) is always greater than 0.

Hence f(x) is an increasing function, which means that it has only one root.

Let x=−1

f(−1)=2(−1)

3

−3(−1)

2

+6(−1)+6

=−2−3−6+6

=−5

Let x=0

f(−1)=2(0)

3

−3(0)

2

+6(0)+6

=6

Hence f(−1)f(0)<0

Which means that α should be in between −1 & 0.

Hence [α]=−1